Resolution enhancement with deblurring by pixel reassignment (DPR)

Improving the spatial resolution of a fluorescence microscope has been an ongoing challenge in the imaging community. To address this challenge, a variety of approaches have been taken, ranging from instrumentation development to image post-processing. An example of the latter is deconvolution, where images are numerically deblurred based on a knowledge of the microscope point spread function. However, deconvolution can easily lead to noise-amplification artifacts. Deblurring by post-processing can also lead to negativities or fail to conserve local linearity between sample and image. We describe here a simple image deblurring algorithm based on pixel reassignment that inherently avoids such artifacts and can be applied to general microscope modalities and fluorophore types. Our algorithm helps distinguish nearby fluorophores even when these are separated by distances smaller than the conventional resolution limit, helping facilitate, for example, the application of single-molecule localization microscopy in dense samples. We demonstrate the versatility and performance of our algorithm under a variety of imaging conditions.

Fig S2 DPR applied to simulated Gaussian PSFs of different sizes with gains 1 and 2. (a) The intensity images and horizontal line profiles of PSFs (with FWHMs of 2, 4, 6, and 8 pixels) before and after DPR gains 1 and 2.Total intensity: the sum of the intensity values at each sub-pixel in the image ('pixel' refers to raw-image pixel size).FWHM on the line profile: calculated FWHM after Gaussian fitting.σ on the line profile: calculated RMS with Gaussian fitting.PSF FWHM: same as used in simulation, local-minimum filter radius: 4 times the FWHM.(b) The correlation between displacement vectors and different gains.Left: raw intensity image of a PSF whose FWHM is 4 pixels.Middle and right: the profiles for raw intensity, weighted gradient, and displacement vector under gain 1 and 2 along the red dashed line indicated on the left; yellow arrows indicate the displacement vectors for sub-pixels located at the half-maximum intensity (middle) and at the quarter-maximum intensity (right) with DPR gain 1; purple arrows indicate the displacement vectors for sub-pixels located at the half-maximum intensity (middle) and at the quartermaximum intensity (right) with DPR gain 2.

Fig S3
Fig S3 The separation accuracy of DPR.(a) DPR applied to simulated images of two point objects separated by different distances.PSF FWHM: 2.35σ, local-minimum filter radius: 8σ.(b) The resolution enhancements of DPR gain 1 and DPR gain 2. (c) The separation errors resulting from DPR.

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Fig S4 DPR applied to fluorescent lines of increasing separation from 0 nm to 390 nm.(a) Raw data acquired by an Airyscan microscope.The full set of line intensity profiles for raw, DPR gain 1, and DPR gain 2. Scale bar: 500 nm.PSF FWHM: 4 pixels, local-minimum filter radius: 7 pixels.(b) Raw data acquired by a confocal microscope.Top: the full set of line images for raw, DPR gain 1, and DPR gain 2. Middle: the full set of line intensity profiles for raw, DPR gain 1, and DPR gain 2. Bottom: the expanded view of four line profiles for raw, DPR gain 1, and DPR gain 2, indicated by the green rectangle.PSF FWHM: 5 pixels, local-minimum filter radius: 9 pixels.Scale bar: 500 nm.

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Fig S5 DPR applied to simulated images of different SNRs.(a) Intensity images with different SNRs of the raw simulated two point objects (left) separated by 160 nm and two line objects (right) separated by 160 nm, without and with DPR.Scale bar: 100 nm.PSF FWHM: 5 pixels, local-minimum filter radius: 17 pixels, gain: 1.(b) Intensity profiles and (c) separation errors of the DPR reconstructed images when averaging over different numbers of frames.Dashed purple lines represent the ground-truth positions.Left: two point objects.Right: two line objects.
Fig S10 Evaluation of preservation of local intensity with DPR (a) Evaluation procedure.Mean values of the difference images for Fig. 4 -confocal images of BPAE cells after DPR (b), Fig. 5 -SoRa images of BPAE cells after DPR gain 1 (c), Fig. 5 -SoRa images of BPAE cells after DPR gain 2 (d), and Fig. 6(a) -simulated images of sarcomere after DPR (e), with standard deviation shown as error bars.

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Fig S11 The overall workflow of DPR.
Fig S12 DPR using gradients compared to with log-PSF gradients.

Table S1
Total counts of images (intensities)

Table S2
Parameters used in DPR, MSSR, and SRRF in the Results